Intervals and Transposition - TCE Music (Tasmania)
“Identify and construct intervals by number and quality, invert them, recognise them by ear, and transpose melodies for different keys and instruments.”
An interval has two parts: a number (count the letter names inclusively) and a quality (major, minor, perfect, augmented or diminished). Perfect intervals are the unison, fourth, fifth and octave; the rest are major or minor. Inverting an interval swaps the number to nine minus the original and flips major to minor and augmented to diminished, while perfect stays perfect. Transposing moves every note by the same interval, keeping the shape but changing the key.
What this dot point is asking
Measuring intervals: number and quality
To name an interval, first count the number. Count the letter names from the lower to the upper note inclusively, so C up to E spans C, D, E, which is a third. The number ignores sharps and flats; it only counts staff positions.
Then find the quality by counting semitones. The unison, fourth, fifth and octave can be perfect, augmented or diminished. The second, third, sixth and seventh can be major, minor, augmented or diminished. A major interval made one semitone smaller becomes minor; a minor made one smaller becomes diminished; a major or perfect made one semitone larger becomes augmented.
A reliable method is to treat the lower note as a tonic. Ask whether the upper note belongs to that major scale. If it does, the interval is major (for 2nd, 3rd, 6th, 7th) or perfect (for 4th, 5th, 8ve). If the upper note is a semitone lower than the scale degree, the interval is minor or diminished.
The number of an interval counts letter names inclusively (C to G is a fifth). The quality (perfect, major, minor, augmented, diminished) measures the exact size in semitones. You always state both, for example a minor sixth or a perfect fifth.
Common intervals to memorise
Some semitone counts are worth knowing instantly: minor second is 1 semitone, major second is 2, minor third is 3, major third is 4, perfect fourth is 5, tritone (augmented fourth or diminished fifth) is 6, perfect fifth is 7, minor sixth is 8, major sixth is 9, minor seventh is 10, major seventh is 11, octave is 12.
Inversion
Inverting an interval means moving the lower note up an octave (or the upper note down) so they swap positions. The numbers always add to nine: a third inverts to a sixth, a fourth to a fifth, a second to a seventh. Quality flips too: major becomes minor, minor becomes major, augmented becomes diminished and diminished becomes augmented, while perfect stays perfect. So a major third inverts to a minor sixth, and a perfect fifth inverts to a perfect fourth.
For any interval and its inversion the two numbers add to nine and the qualities swap (major to minor, augmented to diminished), with perfect remaining perfect. Use this to check your interval naming quickly.
Hearing intervals
Aural tasks ask you to identify intervals by ear. The standard trick is to link each interval to the opening of a well-known tune. A perfect fifth opens many fanfares, a perfect fourth has a strong open sound, a minor third sounds slightly sad, and a major third sounds bright. The tritone is restless and unstable. Practise singing up and down from a given note so you can produce as well as recognise each interval, because the external exam tests both directions.
Transposition
Transposition rewrites music so every note moves by the same interval, preserving the melody's shape and intervals while changing its key. You transpose to suit a singer's range, to make reading easier, or to write for a transposing instrument.
There are two common reasons. To change key, decide the interval between old and new tonic, then move every note and rebuild the key signature. To write for a transposing instrument, remember that a written note sounds at a fixed interval away: a B flat clarinet sounds a major second lower than written, so to keep the same concert pitch you write its part a major second higher.
Step 1: Move each note up the interval
Transpose C D E (in C major) up a major third. C up a major third is E; D up a major third is F sharp; E up a major third is G sharp. So the new notes are E, F sharp, G sharp.
Step 2: Find the new key
Each note rose by the same major third, so the whole passage moves up a major third from C major to E major. Write the new key signature, E major with four sharps, rather than accidentals on every note.
Step 3: Check intervals are preserved
Confirm each letter name moved up two staff positions and that the quality of every interval between the notes is unchanged. Preserved intervals are the proof that the transposition is correct.
Putting it together
Interval work underpins almost everything else in the course: chords are stacks of intervals, transcription depends on hearing them, and transposition relies on applying one interval consistently. Drill number and quality until naming is automatic, learn the rule of nine for inversions, and rehearse aural recognition both up and down. For transposition, always rebuild the key signature rather than writing accidentals on every note.
Students sometimes pick the wrong spelling, calling a note F sharp when the interval requires G flat. The number fixes the letter name first: a third from E must be some kind of G, never an F sharp, even though they sound the same. Get the letter from the number, then adjust the quality with sharps or flats.
Exam-style questions
Questions in the style of TASC exam questions on this dot point, each with a worked answer. They are written by ExamExplained unless tagged "Past paper"; the year shows the paper a question is modelled on.
Practice8 marksFrom the printed two-bar melody, identify the four labelled intervals (a) to (d) by number and quality, then transpose the melody up a perfect fourth and write the new key signature.Show worked answer →
Work each interval in two moves: count letter names inclusively for the number, then count semitones for the quality.
Worked example for one interval: G up to E is five letter names (G, A, B, C, D, E is actually six, so a sixth); G to E is 9 semitones, and a major sixth is 9 semitones, so it is a major sixth. Always state both parts, because a bare "sixth" earns at most half marks.
For the transposition, a perfect fourth up from each note: if the melody is in D major, up a perfect fourth gives G major. Move every letter name up four staff positions (D to G, F sharp to B, A to D) and write the new key signature (G major, one sharp) rather than putting accidentals on every note. Markers reward a correctly rebuilt key signature and consistent spelling.
Practice6 marksExplain, with reference to concert pitch, how you would prepare a part written in concert C for a B flat clarinet, and name the interval and direction of transposition involved.Show worked answer →
A B flat clarinet sounds a major second ( semitones) lower than written. To make it sound at concert pitch, you must write its part a major second higher than the concert-pitch line.
So a passage notated in concert C major is written for the clarinet in D major: every concert note is raised a major second and the key signature gains two sharps.
State the rule explicitly for the marks: "the instrument transposes down a major second, so the written part is a major second above concert pitch." A common error is transposing in the wrong direction, which inverts the whole part. Naming the interval (major second) and the direction (up, when writing the part) is what the marker is checking.